Empirical processes of iterated maps that contract on average

Olivier Durieu

Statistics & Probability Letters, 2013, vol. 83, issue 11, 2454-2458

Abstract: We consider a Markov chain obtained by random iterations of Lipschitz maps Ti chosen with a probability pi(x) depending on the current position x. We assume this system has a property of “contraction on average”, that is ∑id(Tix,Tiy)pi(x)<ρd(x,y) for some ρ<1. In the present note, we study the weak convergence of the empirical process associated to this Markov chain.

Keywords: Iterated random maps; Markov chains; Empirical processes; Weak convergence (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715213002526
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:83:y:2013:i:11:p:2454-2458

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2013.07.003

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().